A Journey Through the Flames of War in the Republican Era

"Let's first look at the case where there is only a small amount of known plaintext. The first letter W of plaintext WETTER is encrypted into E. Its encryption process is as follows: First, it is replaced once through the plugboard (denoted as function p1), then it goes through three rotors (denoted as r), then it goes through the reflector back and goes through the plugboard again (p2), which is written as W->(p1)->r->(p2)->E."

"We know that passing through the power strip twice is just a simple pairwise letter substitution. We can use the following method to infer the power strip settings: Assume -> (p1) = A, and then A is encrypted through three rotors. Since the internal connection structure of the rotors is known, we can reasonably choose a rotor state. Assume that A outputs L after passing through the rotor, that is, A->r = L. Thus, L-> (p2) = E, and we can deduce that LE is connected between L and E in the power strip."

Song Hongfei scribbled his calculations on the blackboard, while Yu Dawei watched intently, his mind racing.

"Thus, by continuing to deduce in the same way using this known plaintext, we can discover other settings of the power strip: KQ, XB, TG, WJ. Here we find a problem. We first assumed WA; W cannot simultaneously connect two letters, A and J, which proves that the setting of WA is incorrect. Then, we continue to deduce -D, iterating in this way, deducing all 26 possibilities. Of course, no connection is also a possibility..."

"If all possibilities are wrong, it means the rotor setting is incorrect. You need to adjust the rotor, try another setting, and repeat the reasoning process above."

Yu Dawei exclaimed, "What a brilliant method! This way, we only need to try the power strip connection 26 times! There are a total of 100,000 possible rotor settings. Although it's still a lot of work, it's achievable!"

Song Hongfei said, "Yes, that's the principle behind the cracking process! However, it takes a long time. There are smarter methods. First, when we find that we have obtained an incorrect result, such as WA and WJ, it means that the connections obtained from the related inferences are all wrong. We don't need to check these connections anymore, which can eliminate a large number of combinations to be checked."

Yu Dawei nodded and said, "Yes, this will greatly reduce the time required!"

Song Hongfei chuckled and said, "But this is still all repetitive manual work. We should hand it over to machines!"

Song Hongfei then drew a schematic diagram on the blackboard and proceeded with the deduction: "We can design a machine that implements the above predictions, such as WA, through a circuit. The circuit will automatically make predictions, and when it reaches WJ, it means that the prediction is wrong. The circuit can quickly find all possible predictions in WA, that is, all wrong results. Then, it will predict another set of rotor settings in turn. A number of hundreds of thousands is not a problem for the circuit."

"It's a process of constantly eliminating incorrect options. In the end, what's left are the settings that didn't cause any errors. You just need to manually check them to see if the results are correct."

Yu Dawei said, "By assigning the most tedious and repetitive tasks to machines, efficiency is greatly improved!"

Song Hongfei added, "If more plaintext like this is obtained, cryptographers call it a 'Crib'. When a letter ring can be formed, there are even more ingenious methods for the machine to use."

Yu Dawei was very interested and said, "Cheat sheet? That's a fitting name."

Song Hongfei deduced: "Let's take WETTER as an example again. If we can deduce the following cheat sheet that forms a ring:

Plaintext WETTER

Ciphertext E R K M G W

In this binary search relationship, plaintext W is first encrypted as E. After the rotor rotates one bit, E is encrypted as R. After the rotor rotates five bits, R is encrypted as W. This is denoted as: W->(r1)->E->(r2)->R->(r6)->W.

Observing the step W -> E, its process through the connector and rotor is W -> p1 -> r -> (p2) -> E. W is first replaced by another letter by the connector, denoted as t1. Then t1 enters the three rotors and is replaced by t2. Finally, t2 passes through the connector again and is replaced by E. The whole process is denoted as: W -> (p) -> t1 -> r -> t2 -> (p) -> E.

In the letter ring WERW, it can be equivalent to the three letters W, E, and R being concatenated end-to-end by three cipher machines, and the result of encryption obtained by using the output of the previous machine as the input of the next machine, which are denoted as WE, ER, and RW respectively.

The entire process is as follows:

W->(p)->t1->r(1)->t2->(p) ->E

->E->(p)->t3->r(2)->t4->(p) ->R

->R->(p)->t5->r(6)->t6->(p) ->W

Because the socket settings remain unchanged throughout the encryption process, t2 passes through the first machine's socket to obtain E, and then E passes through the second socket to obtain t3. Therefore, t2 = t3, and similarly, t4 = t5, t1 = t6. This socket process cancels out the other processes. Thus, the process simplifies to:

W->(p)->t1->r(1)->t2

-＞r(2)-＞t4

-＞r(6)-＞t6-＞(p-＞W

Now, simply input t1, and then try to pass v1 through the rotors r(1), r(2), and r(6) of the three Engma machines to obtain an output t6, and check if t1 = t6. If they are not equal, it means that the current rotor setting is incorrect. If they are equal, it means that the cipher machine setting may be correct, and then the plaintext and ciphertext can be checked manually.

"The output t1 of the power strip is nothing more than 26 possibilities. We can even test it by manufacturing several such series machines and inputting 26 letters at the same time," Song Hongfei said slowly.

Yu Dawei was utterly dumbfounded.

He seemed to have been enlightened, his expression one of sudden realization, his mouth agape: "This, this, this is simply amazing! Using multiple machines to perform parallel calculations, with the output of one machine as the input of the next, the complex processes in between can be canceled out! In other words, it can bypass the interference of a hundred billion power strip results, and the only thing to check is 100,000 rotor settings, which immediately reduces the number to an acceptable range!"

Yu Dawei was completely impressed.

He suddenly looked at Song Hongfei and said, "Sometimes, I really want to take your head and study it to see how you came up with such a brilliant method!"

Although Song Hongfei felt extremely pleased, he still silently thought to himself, "I'm ashamed, I'm ashamed. These cracking methods originated from numerous cryptographers and mathematicians in Poland and Britain before and after World War II. I merely used what was readily available. Of course, some of these also include computer program algorithms that I optimized and improved during my time at the G Military Academy in my later years..."

Song Hongfei solemnly said, "Actually, this is not my idea; it is the result obtained using a computer."

Yu Dawei was stunned for a moment, and remained in shock and thought for a long time.

After a long silence, he said solemnly, "I'm also very fortunate! Thankfully, you are one of us Chinese, not our enemy!"

Yu Dawei added, "It's unbelievable how powerful computers are! Like using the output of a process as input and then canceling each other out, it's something that human thought processes can hardly conceive of."

Song Hongfei said, "Yes, it's like a simple recursive algorithm. It's hard for humans to understand, but computers can process it with ease."

Yu Dawei was taken aback again, then suddenly smiled: "You rascal, these past few days you've been subtly and overtly hinting at things to me. Are you plotting to get the Ordnance Department to increase its investment in computer research and development?"

Song Hongfei also smiled and said, "Commander Yu has keen insight."

Yu Dawei laughed again, "That's why I say we're fortunate! Right now, we're stretched thin in terms of funding, technology, and talent. The Military Commission had some reservations about such a large investment. Fortunately, we have a computer expert like you, which allows our research to keep up with the world's top standards! If those high-ranking officials can realize the power of computers, things will be much easier!"

Yu Dawei then remembered something and said, "I've read your doctoral dissertation on the logical symbol analysis of binary and switching circuits. I've also been thinking that if we conduct in-depth research on this theory and apply and develop it in electronic engineering and computer technology, we would very much like to lead the trend of advanced international technology."

Song Hongfei exclaimed with excitement: "Without a doubt, the development direction of electronic engineering and computers will be binary and electronic! I believe that computers will change the world!"

Yu Dawei, the "Father of Ordnance Industry," was a visionary figure of his time. He also recognized the strategic significance of a country occupying the commanding heights of science and technology.

Yu Dawei pondered for a moment, then said, "I will strongly urge the high-ranking officials of the Military Commission to take this opportunity to increase investment in electronic technology and computer research, and especially to focus on cultivating more scientific and technological talents."

Song Hongfei felt a surge of warmth in his heart. He knew that over the years, this father of the military industry had devoted himself wholeheartedly to the cause, making outstanding contributions to China's modernization of industry, military industry, national defense science and technology, and the cultivation of scientific research talents in the face of difficulties both at home and abroad.

Song Hongfei looked at Yu Dawei with great excitement: "Commander Yu's vision and foresight are a great blessing to our nation."

Both were equally excited and felt a deep mutual respect.

After a long silence, Yu Dawei finally said, "Alright, let's stop praising each other here."

The two looked at each other and burst into laughter.

The feeling of ideals or beliefs stirring in one's heart is so beautiful and so captivating.

Yu Dawei suddenly looked at Song Hongfei again and said, "Based on my understanding of you, I'm wondering if you have some other purpose in going to such lengths to crack the German code?"

Song Hongfei said, "I admire you. It seems nothing can hide from you."

"It seems that's indeed the case!" Yu Dawei laughed. "You want to use this to make a deal with the Germans?"

Song Hongfei made no attempt to hide his intentions, saying, "That's right, we want to make a deal with the Germans!"

Yu Dawei pondered for a long time before saying, "Prepare a report as soon as possible! I'll find some experts from the Military Commission's Secret Telegram Group to assist you. Remember, some secrets must be firmly held in your own hands; you can't easily reveal your trump cards."

"Understood!" Song Hongfei said, "Let's test the waters first!"

Yu Dawei laughed heartily, he was in a great mood: "No one gets up early for nothing, your Song family really knows how to do business! Ah, I was just joking! Don't mind me, don't look at me like that!"